$A_{n-1}$ Gaudin model with open boundaries

TL;DR

This paper analyzes the $A_{n-1}$ Gaudin model with open boundaries using algebraic Bethe ansatz, deriving eigenvalues and Bethe equations for integrable boundary conditions.

Contribution

It introduces a method to diagonalize the Gaudin model with non-diagonal boundary K-matrices and obtains explicit eigenvalues and Bethe ansatz equations.

Findings

Eigenvalues of the Gaudin operators are explicitly derived.

Bethe ansatz equations for the model are established.

The model's integrability with open boundaries is confirmed.

Abstract

The $A_{n-1}$ Gaudin model with integerable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained.